Evaluate
191
Factor
191
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\begin{array}{l}\phantom{21)}\phantom{1}\\21\overline{)4011}\\\end{array}
Use the 1^{st} digit 4 from dividend 4011
\begin{array}{l}\phantom{21)}0\phantom{2}\\21\overline{)4011}\\\end{array}
Since 4 is less than 21, use the next digit 0 from dividend 4011 and add 0 to the quotient
\begin{array}{l}\phantom{21)}0\phantom{3}\\21\overline{)4011}\\\end{array}
Use the 2^{nd} digit 0 from dividend 4011
\begin{array}{l}\phantom{21)}01\phantom{4}\\21\overline{)4011}\\\phantom{21)}\underline{\phantom{}21\phantom{99}}\\\phantom{21)}19\\\end{array}
Find closest multiple of 21 to 40. We see that 1 \times 21 = 21 is the nearest. Now subtract 21 from 40 to get reminder 19. Add 1 to quotient.
\begin{array}{l}\phantom{21)}01\phantom{5}\\21\overline{)4011}\\\phantom{21)}\underline{\phantom{}21\phantom{99}}\\\phantom{21)}191\\\end{array}
Use the 3^{rd} digit 1 from dividend 4011
\begin{array}{l}\phantom{21)}019\phantom{6}\\21\overline{)4011}\\\phantom{21)}\underline{\phantom{}21\phantom{99}}\\\phantom{21)}191\\\phantom{21)}\underline{\phantom{}189\phantom{9}}\\\phantom{21)99}2\\\end{array}
Find closest multiple of 21 to 191. We see that 9 \times 21 = 189 is the nearest. Now subtract 189 from 191 to get reminder 2. Add 9 to quotient.
\begin{array}{l}\phantom{21)}019\phantom{7}\\21\overline{)4011}\\\phantom{21)}\underline{\phantom{}21\phantom{99}}\\\phantom{21)}191\\\phantom{21)}\underline{\phantom{}189\phantom{9}}\\\phantom{21)99}21\\\end{array}
Use the 4^{th} digit 1 from dividend 4011
\begin{array}{l}\phantom{21)}0191\phantom{8}\\21\overline{)4011}\\\phantom{21)}\underline{\phantom{}21\phantom{99}}\\\phantom{21)}191\\\phantom{21)}\underline{\phantom{}189\phantom{9}}\\\phantom{21)99}21\\\phantom{21)}\underline{\phantom{99}21\phantom{}}\\\phantom{21)9999}0\\\end{array}
Find closest multiple of 21 to 21. We see that 1 \times 21 = 21 is the nearest. Now subtract 21 from 21 to get reminder 0. Add 1 to quotient.
\text{Quotient: }191 \text{Reminder: }0
Since 0 is less than 21, stop the division. The reminder is 0. The topmost line 0191 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 191.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}